The New Sudoku Players' Forum

by **dxSudoku** » Mon Aug 30, 2021 12:47 am

I have another question if someone is willing to answer it. If you have 22 givens in your constellations of givens, and given that there are 81 cells, how many unique patterns of constellations are there with 81 givens. Is this simply 81 choose 2 combinatorics? 2 meaning either the given is present in the constellation of givens or the cells is empty. I'm just okay at math so I'm not that confident in my thinking.

by **marek stefanik** » Mon Aug 30, 2021 7:43 am

There is no (known) sudoku that would require brute-force as a solving step – otherwise you couldn't get a meaningful rating function. Most rating systems add another layer of chains to solve the hardest puzzles.
Only puzzles with exactly one solution are considered valid – this is checked for before attempting to rate the puzzle and it is indeed done by brute-force.
For more insight into the creation process, check out this post by mith.

dxSudoku wrote:If you have 22 givens in your constellations of givens, and given that there are 81 cells (...) either the given is present in the constellation of givens or the cells is empty.

You have 81 choose 22 ways to organise them, some of which cannot produce a unique solution when filled with digits (such as all givens in one band).

by **mith** » Wed Sep 01, 2021 2:48 pm

Code: Select all: 31c ........1.....2.3..34..5.....1.6..736.34.781.78....6....8...1.631..86.4.4.67...8. ED=11.6/1.2/1.2

This one isn't too surprising since we were already in +dfc range, but finally found one.

by **mith** » Wed Sep 01, 2021 2:52 pm

Code: Select all: 36c ...........1..2.34..2.1356..17.86..3.6.2.1.8.2.873.6...7..28...12.36..7.8.61.73.. ED=10.6/1.2/1.2

(A few 35c as well.)

by **urhegyi** » Fri Sep 03, 2021 2:43 pm

What is the highest sudoku rating ever? I thought it was below the theoretical 12.0. But now i'm confused. I just rated a sudoku-x (with diagonal blocks) for over 18,5 hours and this was the result:

Hidden Text: Show

re-rated in 1.5 hours with the newest version:

Hidden Text: Show

by **mith** » Fri Sep 03, 2021 3:10 pm

11.9 is the high for classic. With additional constraints, you can go higher (anti-knight is another with a puzzle known to be at least 12.6 but probably higher).

by **999_Springs** » Fri Sep 03, 2021 4:15 pm

eleven wrote:
heetbeet wrote:https://www.dcc.fc.up.pt/~acm/sudoku.pdf

It's really impressing, that about 10 years after people in this forum posted free programs, which solve each known puzzle (100 times harder than the author's ones) in a split second, a paper is written where it says
"No puzzle requiring more than 3 minutes (in a relatively old computer) was found."

just saw this. this is hilarious. i checked it out and solved their "most difficult puzzle" by hand in 12.5 minutes using only hidden pairs and locked candidates. a speed solver on here like strmckr or qiuyanzhe or maybe sclt might be able to beat the computer's best time - and by the standards of that paper that would mean humans are better than computers at sudoku :lol:

heetbeet seems to also be interested in some sudoku variants like killer sudokus:

heetbeet wrote:We also used a ton of Killer Sudokus, Calcudokus, Kakuros and Fill-a-Pix for further colouring in our puzzle database.

i would also be interested in what happens with those; there is no widely accepted means of defining difficulty of a killer sudoku other than time to brute force, or number of guesses needed. unlike normal sudokus which solve with brute force in microseconds, the puzzles in this thread need a few minutes to solve with brute force

and unlike this author's example these killer puzzles seem to be impossible for humans too

by **RSW** » Fri Sep 03, 2021 8:30 pm

999_Springs wrote:just saw this. this is hilarious. i checked it out and solved their "most difficult puzzle" by hand in 12.5 minutes using only hidden pairs and locked candidates. a speed solver on here like strmckr or qiuyanzhe or maybe sclt might be able to beat the computer's best time - and by the standards of that paper that would mean humans are better than computers at sudoku

Just tried it on my solver, which I'm sure is nowhere near as efficient as the solvers written by other forum members. My solver took 110 milliseconds using basics only.
Solution:

Hidden Text: Show

BTW, I would argue that the term "brute force" has been used rather inaccurately in this discussion. In a puzzle that has been solved using logical moves until an impasse is reached, and then the solver has no remaining strategies except to make a guess, this is not a brute force move. It is a trial and error move, or T&E. To me, brute force refers to a solving technique which never involves any of the recognized Sudoku logic based moves, but rather makes nothing but guesses from the very first move. Brute force is a subset of T&E. Maybe I'm splitting hairs, because experienced human players are generally against any sort of T&E move, brute force or not.

by **m_b_metcalf** » Fri Sep 10, 2021 9:24 am

urhegyi wrote:What is the highest sudoku rating ever? I thought it was below the theoretical 12.0. But now i'm confused. I just rated a sudoku-x (with diagonal blocks) for over 18,5 hours and this was the result:

This puzzle is not new and the result is wrong, see http://forum.enjoysudoku.com/x-sudoku-extreme-t34714-15.html#p309280. Mike

by **mith** » Sat Sep 11, 2021 8:40 pm

Code: Select all: 33c ........1....23....24.....5.67..4.8.3.2.86...84..7.6.3.76.38...28.74.3.64.3..2.7. ED=11.3/1.2/1.2

(Also some new 11.7s in the 22-23c range, and a ton of 11.6s in the 27-30c range. I'll post a more complete update once I get through the current good neighborhood.)

by **999_Springs** » Sun Sep 12, 2021 11:19 am

here is an old-fashioned ascii histogram of chain lengths of the 11.8 and 11.9 puzzles in 1to9only's post (by the way, thanks for doing this!)

Code: Select all: node count rounded down to nearest 16 SE nodes | sudokus ----------+---------------------- 11.8 256 | ######### 272 | ############## 288 | ################ 304 | ######### 320 | ##### 336 | ### 352 | ## 368 | # Mike's 20 ----------+---------------------- 11.9 384 | ##### 400 | 416 | # Golden Nugget 432 | # eleven's Patience 448 | 464 | ## champagne dry; Obi-Wahn 2015 480 | 496 | ----------+---------------------- 12.0 512 |

from this we can see that:

5 of the 9 11.9's only barely make it into the 11.9 category, with a longest chain of less than 400 nodes, putting them into the lowest 1/8th of possible longest chain lengths for 11.9's (384 is the threshold)
no puzzle exists in the top 1/4 of possible longest chain lengths for 11.9's
the closest puzzle to SE 12.0 is Obi-Wahn's 11.9, which is the most recently found 11.9, found in 2015
81% of 11.8's are in the lower half of possible longest chain lengths for 11.8's
Mike's 20 clue is the 11.8 that is closest to 11.9

mith wrote:
Code: Select all
33c ........1....23....24.....5.67..4.8.3.2.86...84..7.6.3.76.38...28.74.3.64.3..2.7. ED=11.3/1.2/1.2

this starts with 4 hidden singles so when you fill them in you break Mauricio's 14 year old record from January 2007 for the hardest puzzle with 37 clues, which was his symmetric 11.2. nice!

RSW wrote:BTW, I would argue that the term "brute force" has been used rather inaccurately in this discussion.

i referred to "brute force" only in the context of solving killer sudokus, and called it that because that was what the solvers called it in the thread that i linked. i don't have those killer sudoku solvers installed but my understanding is that what they describe as "brute force" agrees with what you are saying, in other words, nested guesses using DFS or something similar to determine puzzle validity as quickly as possible. in this context, the killer sudokus in that thread take a few minutes to determine that the solution is unique. here is an example of a browser based brute force killer sudoku solver which is the fastest one i know of

by **mith** » Sun Sep 12, 2021 4:51 pm

999_Springs wrote:
mith wrote:
Code: Select all
33c ........1....23....24.....5.67..4.8.3.2.86...84..7.6.3.76.38...28.74.3.64.3..2.7. ED=11.3/1.2/1.2

this starts with 4 hidden singles so when you fill them in you break Mauricio's 14 year old record from January 2007 for the hardest puzzle with 37 clues, which was his symmetric 11.2. nice!

Yeah, I need to run my singles expander on all these hard puzzles, I've probably broken some more of the most-clues-for-given-ER by now.

by **RSW** » Sun Sep 12, 2021 4:57 pm

999_Springs wrote:
RSW wrote:BTW, I would argue that the term "brute force" has been used rather inaccurately in this discussion.

i referred to "brute force" only in the context of solving killer sudokus, and called it that because that was what the solvers called it in the thread that i linked. i don't have those killer sudoku solvers installed but my understanding is that what they describe as "brute force" agrees with what you are saying, in other words, nested guesses using DFS or something similar to determine puzzle validity as quickly as possible. in this context, the killer sudokus in that thread take a few minutes to determine that the solution is unique. here is an example of a browser based brute force killer sudoku solver which is the fastest one i know of

Actually, I was referring mainly to dxSudoku's use of the term in both this thread and another recent thread. But, as I said, I'm probably splitting hairs.

by **hendrik_monard** » Mon Sep 13, 2021 3:17 pm

mith wrote:11.9 is the high for classic. With additional constraints, you can go higher (anti-knight is another with a puzzle known to be at least 12.6 but probably higher).

The sudoku in the hidden image of the post by urhegyi » Fri Sep 03, 2021 3:43 pm ,with rating 12.6 is the following:
..1...2....23....44........5.3....6..1......5..6..........78.......9.....7...1.9.
This sudoku has multiple solutions (at least 5000). Isn't it amazing that Sudoku Explainer 1.2.1 tells that "this sudoku can be solved using the following logical methods..."
I would expect that in the case of a sudoku with multiple solutions, no solution can be found with logical reasoning. Or am I missing something?

by **m_b_metcalf** » Mon Sep 13, 2021 4:31 pm

hendrik_monard wrote:
The sudoku in the hidden image of the post by urhegyi » Fri Sep 03, 2021 3:43 pm ,with rating 12.6 is the following:
..1...2....23....44........5.3....6..1......5..6..........78.......9.....7...1.9.
This sudoku has multiple solutions (at least 5000). Isn't it amazing that Sudoku Explainer 1.2.1 tells that "this sudoku can be solved using the following logical methods..."
I would expect that in the case of a sudoku with multiple solutions, no solution can be found with logical reasoning. Or am I missing something?

Please scroll back to my previous post about this X-sudoku. M.

[Edit: treated as a standard puzzle, it has 3194507 solutions.]

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